The bottom row of the final tableau for a linear programming problem will have zeros as entries in the columns corresponding to the basic variables that are “in” the solution. There may also be zeros in some of the other columns in this bottom row. When this happens, the optimal solution will not be unique since these other variables could be brought into the solution without changing the value of the objective function.a. Find all of the optimal solutions to the following problem:

b. Describe the set of solutions geometrically.

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Maximize Subject to 4x₁ + 5x2-x3 x₁ + 2x2x3 ≤ 16 x₁ + x₂ < 12 2x1 + 2x2 + x3 ≤ 36 and X₁ ≥ 0, X₂ ≥ 0, X3 ≥ 0.